New Voltage

Two reasons you don't want to power accessories directly rom the alternator;

1. The output of an alternator is AC (hence the name alternator) and diodes are used to rectifiy the output. But, it's still a pulsing DC signal which can cause problems with some accessories like stereos. The battery acts like a big capacitor so you get clean DC power when you take your power from the battery.

2. You are shunting off a portion of the alternator's output to run the lights. This is confusing the voltage regulator and is the reason you get 12-13 volts (which is not enough to charge the battery consistently) with the lights on and 14 with the lights off.

FWIW, I have never heard anyone recomend taking power directly from the alternator output terminal to power an accessory.